Youtube is telling me that I should "prepare video for internet streaming." I know how to do that in iMovie (and don't ever want to be stuck there again) but I'm not finding any options to do so in After Effects. Is it possible to do so, or should I be using some other format than H.264?

There are a bunch of threads on this in this forum. Basically you use the YouTube preset in the Adobe Media Encoder. You can open your AE project directly inside AME or you may render to a production codec from AE and use that in AME. DO NOT use AE to render h.264 files that are for anything other than a quick preview.